MinT - Information on Result #1703527

Information on Result #1703527

Linear OOA(2²¹⁷, 74904, F₂, 8, 23) (dual of [(74904, 8), 599015, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹⁷, 74904, F₂, 7, 23) (dual of [(74904, 7), 524111, 24]-NRT-code), using

OOA 7-folding [i] based on linear OA(2²¹⁷, 524328, F₂, 23) (dual of [524328, 524111, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2²¹⁷, 524333, F₂, 23) (dual of [524333, 524116, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
    1. linear OA(2²¹⁰, 524288, F₂, 23) (dual of [524288, 524078, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(2¹⁷², 524288, F₂, 19) (dual of [524288, 524116, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(2⁷, 45, F₂, 3) (dual of [45, 38, 4]-code or 45-cap in PG(6,2)), using
      - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²¹⁸, 74904, F₂, 8, 23) (dual of [(74904, 8), 599014, 24]-NRT-code)	[i]		OOA Duplication